In this section, we prove Theorem \(\ref {d-Marker}\) , which can be considered as a weak version of Rokhlin Lemma for free Borel \({\mathbb {Z}}^d\) -action. Before we prove Theorem \(\ref {d-Marker}\)  it is useful to discuss its one-dimensional version (Theorem \(\ref {Marker1}\) ) due to B. Weiss ([1]}). We have included the proof of Theorem \(\ref {Marker1}\)  for completion. The proof of Theorem \(\ref {Marker1}\)  is taken from [2]}.
